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Differential Equations 00 | 4th Edition | ISBN: 9780495561989 | Authors: Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall
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(Damped, forced oscillator) Using the same value of k1 as

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QUESTION:

(Damped, forced oscillator) Using the same value of k1 as in Part 1, study the solutions of d2 y dt2 + b dy dt + k1 y = 10 + 0.1 sint. You may use analytic or numerical methods to study the relationship between the amplitude of the solutions for 0 5 for different values of b. Graph the amplitude as a function of for different b values. What happens to these graphs as b 0?

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QUESTION:

(Damped, forced oscillator) Using the same value of k1 as in Part 1, study the solutions of d2 y dt2 + b dy dt + k1 y = 10 + 0.1 sint. You may use analytic or numerical methods to study the relationship between the amplitude of the solutions for 0 5 for different values of b. Graph the amplitude as a function of for different b values. What happens to these graphs as b 0?

ANSWER:

Problem 1

(Damped, forced harmonic oscillator) Using the same value of  as in Part 1, study the solutions of

 

                                                         Step by step solution

Step 1 of 4

Given condition of oscillator is:

 

The solution of this will be of the form:

 

Where:

 = Complementary function

 = Particular Integral

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